In the book it's explained as 'There's so much bad blood here that whichever one he picks, the other one will try to Murder the Hypotenuse anyway, so might as well have the fight open and aboveboard and over with as quickly as possible'.
Why did Grant decide to shoot Bond several times? The entire plan relied on it looking like he had committed suicide.
Because Grant was a psycho which was the reason Kronsteen's elaborate plan failed.
Besides, he can always make it look like Tatiana was the suicide. Or have Bond's "suicide" be so messy (like jumping off the train into the water or something) that no one gets a good look at the body.
Are we ever told which of the Gypsy girls get to marry the Prince?
They both spend the night with Bond. Win-win-win! Except for the prince, that is.
My guess is, since the green-clothed one sees Bond off right at the car while the other watches from the porch, it was her.
Why is Kronsteen such a chessmaster? Does it take a member of Mensa to come up with the idea of having a hot girl lure Bond?
That wasn't the plan. The plan was to have a staged defection which the British would suspect as a trap but not suspect that SPECTRE was behind and to ratchet up the tensions between Russian and British intelligence to the point that SPECTRE would never be suspected. This depended on a whole host of people including Tatania, Bond and the various intelligence services being deceived and people acting in exactly the right way, hence why a chessmaster's mind was needed.